Moan.speak is used to insert a single message into the message queue, and therefore should only be called once per message - by putting Moan.speak into love.draw you are inserting new message every frame (which would probably cause the game to crash eventually)
Moan.update updates the library (which you forgot to add)
Moan.draw is used to draw the messages in the message queue

require("lovesplash/lovesplash")
local Moan = require("Moan")
state = "lovesplash"
function love.load()
-- Insert a message into the message queue
-- Message shown when Moan.draw called (in menu state)
Moan.speak("Title", {"Hello world!", "It's me;--Möan.lua"})
end
function love.draw()
if state == "lovesplash" then
lovesplash.draw()
else if state == "menu" then
Moan.draw()
end
end
function love.update(dt)
if state == "lovesplash" then
lovesplash.update(dt)
if lovesplash.done() then
state = "menu"
Moan.update(dt)
end
end
end
function love.keypressed()
if state == "lovesplash" then
lovesplash.stop()
else if state == "exit" then
love.event.quit()
else
end
end
end
function love.mousepressed()
if state == "lovesplash" then
lovesplash.stop()
else if state == "exit" then
love.event.quit()
else
end
end
end

Also I'd recommend reading the example main.lua (https://github.com/ttxi/Moan.lua/blob/master/main.lua) as it shows how to use the library and is pretty heavily commented.
I apologise in advance for how awkward the library is to use - I wrote it last year when my programming skills were pretty bad, I'm planning a rewrite in the near future for LOVE 11.

Hey everyone, I went looking for this library today and found that the repo and the user's github account has been deleted so I created and mirrors the code from the original .love file in this thread https://github.com/tanema/Moan.lua. If anyone has a more recent version of it with bug fixes please either let me know or open a PR.